Put the drained lobster meat in a non-reactive and heat resistant container that holds at least 2 quarts in volume.
In a separate pot heat water with remaining ingredients and bring to a boil. When boiling, turn off heat and pour the boiling liquid over the cold cracked lobster. Set a timer for 6 minutes and remove cooked meat from warm liquid with a slotted spoon and set to dry on a plate lined with a paper towel. Chill in refrigerator for 30 minutes.
For the dressing, mix mayo, dill, and lemon juice together in bowl. Season to taste with salt and pepper. Mix dressing a bit at a time into chilled lobster meat until desired consistency is reached.
Melt butter in pan over medium heat and griddle both sides of the two hot dog buns until golden brown on both sides and the interior of the bun is soft and warm. Split the lobster salad between the two buns and enjoy!